The hybrid direct carbon fuel cells (DCFCs) have drawn wide attention in generating electrical energy directly from carbon. Recent research has shown promising high peak power density, however, no good stability performance of this hybrid DCFC was presented. One of the concerns relating to the present hybrid concept is the stability of solid electrolyte in contact with corrosive molten carbonates eutectics. In this study, high temperature exposure tests of YSZ and SDC in the molten carbonates eutectics were conducted to characterize the corrosion as well as the effect of different atmosphere conditions on the stability of YSZ and SDC using scanning electron microscopy, X-ray diffraction, temperature programmed reaction experiments with a mass spectrometer and AC impedance spectroscopy. The results obtained in this study confirm the YSZ and SDC corrosion in the molten carbonates eutectics. YSZ is less corrosion resistant in the molten carbonate eutectics than SDC, but the mechanisms of YSZ and SDC corrosion reactions in the molten carbonates eutectics are different.